Neither 4 nor 5 are necessarily required in practice. I converted an employers monorepo to reproducible semi-recently, without eliminating any math libraries, just forcing the compiler to make consistent implementation choices across platforms.

Indeed, you can't do that kind of hsum. Still, haven't run into that behavior in practice (and given that I maintain a FP reproducibility test suite, I've tried). Would be open to any way you can suggest to replicate that with the usual GCC/clang etc.